few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Compute fluently with multi-digit numbers and find common factors and multiples.

Represent complex numbers and their operations on the complex plane.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Apply and extend previous understandings of numbers to the system of rational numbers.

Reason quantitatively and use units to solve problems.

Represent and model with vector quantities.

Perform operations on matrices and use matrices in applications.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Perform arithmetic operations with complex numbers.

Extend the properties of exponents to rational exponents.

Perform operations on vectors.

Use complex numbers in polynomial identities and equations.

Use properties of rational and irrational numbers.
problem_activity: Activity
Students reason abstractly and quantitatively about temperatures over time graphed on coordinate axes (MP2). The goal of this activity is for students to use inequalities to describe the location of points on a coordinate grid in one direction. This activity also introduces the idea of vertical difference on the coordinate plane using a familiar context. Students may use previous strategies such as counting squares, but are not expected to explicitly add or subtract using negative numbers.
Launch
Arrange students in groups of 2. Allow students 3–4 minutes of quiet work time and 1–2 minutes to check results with their partner. Follow with a whole-class discussion.
Engagement: Develop Effort and Persistence.
Connect a new concept to one with which students have experienced success. For example, remind students about the sea levels and elevation number line representations.
Supports accessibility for: Social-emotional skills; Conceptual processing
Student Facing
The coordinate plane shows the high and low temperatures in Nome, Alaska over a period of 8 days. The axis labeled
\(T\)
represents temperatures in degrees Fahrenheit. The axis labeled
\(d\)
represents the day.
[IMG]
What was the warmest high temperature?
Write an inequality to describe the high temperatures,
\(H\)
, over the 8-day period.
What was the coldest low temperature?
Write an inequality to describe the low temperatures,
\(L\)
, over the 8-day period.
On which day(s) did the
largest
difference between the high and low temperatures occur? Write down this difference.
On which day(s) did the
smallest
difference between the high and low temperatures occur? Write down this difference.
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
Before doing this problem, do the problem about taxicab distance in an earlier lesson.
The point
\((0,3)\)
is 4 taxicab units away from
\((\text{-}4,3)\)
and 4 taxicab units away from
\((2,1)\)
.
Find as many other points as you can that are 4 taxicab units away from
both
\((\text{-}4,3)\)
and
\((2,1)\)
.
Are there any points that are 3 taxicab units away from both points?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Because the high temperature on day 7 was positive and the low temperature was negative, some students may not notice that the difference was 10 degrees on this day as well. Consider prompting them to use tracing paper to compare the temperature differences on days 6 and 7.
Activity Synthesis
This discussion should lead to two key takeaways. First, students express the range of values for the low and high temperatures using inequalities. Second, students share strategies for finding a difference between two values on the coordinate plane.
Ask students to share their inequalities for
\(H\)
and
\(L\)
. It is expected that students have inequalities that describe the maximum high temperature for
\(H\)
and the minimum low temperature for
\(L\)
, but the discussion should bring out that each variable has 4 statements that capture its possible values:
\(L>\text-3\)
,
\(L=\text-3\)
,
\(L < 26\)
, and
\(L=26\)
for the variable
\(L\)
and
\(H>2\)
,
\(H=2\)
,
\(H < 28\)
, and
\(H=28\)
for the variable
\(H\)
.
Ask students to share their strategies for finding the vertical distance between points. Push them to explain how they took the scale of the vertical axis into account. Invite students to explain how they used the context to make sense of their answers.
Listening, Speaking: MLR8 Discussion Supports.
To support students in producing statements about details in the inequalities, provide sentence frames for students to use when they explain their reasoning to their peers, such as: “This inequality should/should not also be equal to because _____”, “A situation uses an equal sign when _____”, “I know that the inequality _____ is correct because _____.”
Design Principle(s): Support sense-making


correct_option_index: 3